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How to create a program to compute the Hii of the Hat Marix in matlab?

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amj
amj 2018-1-10
编辑： amj 2018-1-11
I'm facing with the problem to compute the Hii of the Hat Matrix at shown in the picture.
Can anyone help me on how to compute? It is supposed to get a single values. However, in my code, it is appeared as 2x2 matrix. Thanks in advance
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amj
amj 2018-1-10
编辑：amj 2018-1-10
This is the code without using csv file:
a = [1 20;1 30;1 40]
for i = 1:length(a)
disp(a(i,:)'.*(a'*a).*a(i,:))
end
But, the result i got as 2x2 matrix not as expected

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the cyclist
the cyclist 2018-1-10
Is this what you want?
x = rand(10,1);
i = 3;
x(i)' .* x'*x .* x(i)
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the cyclist
the cyclist 2018-1-10
I misinterpreted your notation in the example. I believe you can calculate the diagonal element as
a = [1 20;1 30;1 40]
i = 3;
Hii = a(i,:) * inv(a'*a) * a(i,:)'
and the full H matrix as
H = a * inv(a'*a) * a'
There is probably a more efficient way to calculate that, rather than using the full inverse, but I am too lazy to figure it out.

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